MoET: Mixture of Expert Trees and its Application to Verifiable Reinforcement Learning

Rapid advancements in deep learning have led to many recent breakthroughs. While deep learning models achieve superior performance, often statistically better than humans, their adaption into safety-critical settings, such as healthcare or self-driving cars is hindered by their inability to provide safety guarantees or to analyze the inner workings of the model. We present MoET, a novel model based on Mixture of Experts, consisting of decision tree experts and a generalized linear model gating function. While decision boundaries of decision trees (used in an existing verifiable approach), are axis-perpendicular hyperplanes, MoET supports hyperplanes of arbitrary orientation as the boundaries. To support non-differentiable decision trees as experts we formulate a novel training procedure. In addition, we introduce a hard thresholding version, MoET_h, in which predictions are made solely by a single expert chosen via the gating function. Thanks to that property, MoET_h allows each prediction to be easily decomposed into a set of logical rules. Such rules can be translated into a manageable SMT formula providing rich means for verification. While MoET is a general use model, we illustrate its power in the reinforcement learning setting. By training MoET models using an imitation learning procedure on deep RL agents we outperform the previous state-of-the-art technique based on decision trees while preserving the verifiability of the models.